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Ecological inference techniques: an empirical evaluation using data describing gender and voter turnout at New Zealand elections, 1893–1919

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  • Irene L. Hudson
  • Linda Moore
  • Eric J. Beh
  • David G. Steel

Abstract

Summary. The difference, if any, between men's and women's voting patterns is of particular interest to historians of gender and politics. For elections that were held before the introduction of opinion surveying in the 1940s, little data are available with which to estimate such differences. We apply six methods for ecological inference to estimate men's and women's voting rates in New Zealand (NZ), 1893–1919. NZ is an interesting case‐study, since it was the first self‐governing country where women could vote. Furthermore, NZ officials recorded the voting rates of men and women at elections, making it possible to compare estimates produced by methods for ecological inference with known true values, thus testing the efficacy of different methods for ecological inference for this data set. We find that the most popular methods for ecological inference, namely Goodman's ecological regression and King's parametric method, give poor estimates, as does the much debated neighbourhood method. However, King's non‐parametric method, Chambers and Steel's semiparametric method and the Steel, Beh and Chambers homogeneous approach all gave good estimates that were close to the known values, with the homogeneous approach performing best overall. The success of these methods in this example suggests that ecological inference may be a viable option when investigating gender and voting. Moreover, researchers using ecological inference in other fields may do well to consider a range of statistical methods. This work is a significant NZ contribution to historical politics and the first quantitative contribution, in the area of NZ gender and politics.

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  • Irene L. Hudson & Linda Moore & Eric J. Beh & David G. Steel, 2010. "Ecological inference techniques: an empirical evaluation using data describing gender and voter turnout at New Zealand elections, 1893–1919," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 173(1), pages 185-213, January.
  • Handle: RePEc:bla:jorssa:v:173:y:2010:i:1:p:185-213
    DOI: 10.1111/j.1467-985X.2009.00609.x
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    References listed on IDEAS

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    1. Ian Westbrooke & Lisa Jones, 2002. "Applications: Imputation of MĀori Descent for Electoral Calculations in New Zealand," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 44(3), pages 257-265, September.
    2. Adam N. Glynn & Jon Wakefield & Mark S. Handcock & Thomas S. Richardson, 2008. "Alleviating linear ecological bias and optimal design with subsample data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(1), pages 179-202, January.
    3. Nicky Best & Samantha Cockings & James Bennett & Jon Wakefield & Paul Elliott, 2001. "Ecological regression analysis of environmental benzene exposure and childhood leukaemia: sensitivity to data inaccuracies, geographical scale and ecological bias," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(1), pages 155-174.
    4. Imai, Kosuke & Lu, Ying & Strauss, Aaron, 2008. "Bayesian and Likelihood Inference for 2 × 2 Ecological Tables: An Incomplete-Data Approach," Political Analysis, Cambridge University Press, vol. 16(1), pages 41-69, January.
    5. D G Steel & D Holt, 1996. "Rules for Random Aggregation," Environment and Planning A, , vol. 28(6), pages 957-978, June.
    6. Jon Wakefield, 2004. "Ecological inference for 2 × 2 tables (with discussion)," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 167(3), pages 385-445, July.
    7. M Tranmer & D G Steel, 1998. "Using Census Data to Investigate the Causes of the Ecological Fallacy," Environment and Planning A, , vol. 30(5), pages 817-831, May.
    8. R. L. Chambers & D. G. Steel, 2001. "Simple methods for ecological inference in 2×2 tables," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(1), pages 175-192.
    9. Christopher Jackson & And Nicky Best & Sylvia Richardson, 2008. "Hierarchical related regression for combining aggregate and individual data in studies of socio‐economic disease risk factors," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(1), pages 159-178, January.
    10. Andrew Gelman & David K. Park & Stephen Ansolabehere & Phillip N. Price & Lorraine C. Minnite, 2001. "Models, assumptions and model checking in ecological regressions," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(1), pages 101-118.
    11. Jon Wakefield, 2004. "Ecological inference for 2 × 2 tables," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 167(3), pages 385-425, July.
    12. Ori Rosen & Wenxin Jiang & Gary King & Martin A. Tanner, 2001. "Bayesian and Frequentist Inference for Ecological Inference: The R×C Case," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 55(2), pages 134-156, July.
    13. Gary King & Ori Rosen & Martin A. Tanner, 1999. "Binomial-Beta Hierarchical Models for Ecological Inference," Sociological Methods & Research, , vol. 28(1), pages 61-90, August.
    14. David A. Freedman & Stephen P. Klein & Jerome Sacks & Charles A. Smyth & Charles G. Everett, 1991. "Ecological Regression and Voting Rights," Evaluation Review, , vol. 15(6), pages 673-711, December.
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    Cited by:

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    2. Jones, Daniel B. & Troesken, Werner & Walsh, Randall, 2017. "Political participation in a violent society: The impact of lynching on voter turnout in the post-Reconstruction South," Journal of Development Economics, Elsevier, vol. 129(C), pages 29-46.

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